The Cyclic Category, Tor and Ext Interpretation

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 301)


Simplicial objects in an arbitrary category C can be described as functors from the category of non-decreasing maps Δ op to C. Similarly one can construct a category, denoted ΔC and called Connes cyclic category, such that a cyclic object in C can be viewed as a functor from ΔC op to C. The cyclic category ΔC was first described by Connes [1983, where it is denoted Λ or ΔK] who showed how it is constructed out of Δ and the finite cyclic groups.


Simplicial Group Symmetric Group Simplicial Module Braid Group Cyclic Module 
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Bibliographical Comments on Chapter 6

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique AvancéeCentre National de la Recherche ScientifiqueStrasbourgFrance

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